to that of it, is called negative of the given vector. For example, vector is negative of the vector , and written as = – Remark The vectors defined above are such that any of them may be subject to its parallel displacement without changing its magnitude and direction. Such vectors are called free vectors . Throughout this chapter, we will be dealing with free vectors only.
Example Represent graphically a displacement of km, ° west of south. Solution The vector represents the required displacement (Fig . ). Example Classify the following measures as scalars and vectors.
(i) seconds (ii) cm Fig . Fig . (iii) Newton (iv) km/hr (v) g/cm (vi) m/s towards north Solution (i) Time-scalar (ii) Volume-scalar (iii) Force-vector (iv) Speed-scalar (v) Density-scalar (vi) Velocity-vector Example In Fig . , which of the vectors are: (i) Collinear (ii) Equal (iii) Coinitial Solution (i) Collinear vectors : (ii) Equal vectors : (iii) Coinitial vectors : EXERCISE .
. Represent graphically a displacement of km, ° east of north. . Classify the following measures as scalars and vectors.
(i) kg (ii) meters north-west (iii) ° (iv) watt (v) – coulomb (vi) m/s . Classify the following as scalar and vector quantities. (i) time period (ii) distance (iii) force (iv) velocity (v) work done . In Fig .
(a square), identify the following vectors. (i) Coinitial (ii) Equal (iii) Collinear but not equal . Answer the following as true or false. (i) and – are collinear.
(ii) Two collinear vectors are always equal in magnitude. (iii) Two vectors having same magnitude are collinear. (iv) Two collinear vectors having the same magnitude are equal. Fig .
. Addition of Vectors A vector simply means the displacement from a point A to the point B. Now consider a situation that a girl moves from A to B and then from B to C (Fig . ).
The net displacement made by the girl from point A to the point C, is given by the